From a given sample of uniform wire, two circular loops `P` and `Q` are made, `P` of radius `r` and `Q` of radius `nr`. If the M.I. of `Q` about its axis is four times that of `P` about its axis (assuming the wire to be of diameter much smaller than either radius), the value of n is

Options

A. `(4)^(2/3)`
B. `(4)^(1/3)`
C. `(4)^(1/2)`
D. `(4)^(1/4)`

Answer

B

Explanation

Given that `I_(Q)=4I_(P)`
Here `I="mass" xx("radius")^(2)`. If `s` is the linear mass density (mass length) of the wire, then
`sigmaxxpi(nr)xxn^(2)r^(2)=4(sigmaxx2pixr^(2))`
`implies n^(3)=4impliesn=(4)^(1/3)`